A066086 Greatest common divisor of product (p-1) and product (p+1), where p ranges over distinct prime divisors of n; a(n) = gcd(A048250(n), A173557(n)).

1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 6, 8, 1, 2, 2, 2, 2, 4, 2, 2, 2, 2, 6, 2, 6, 2, 8, 2, 1, 4, 2, 24, 2, 2, 6, 8, 2, 2, 12, 2, 2, 8, 2, 2, 2, 2, 2, 8, 6, 2, 2, 8, 6, 4, 2, 2, 8, 2, 6, 4, 1, 12, 4, 2, 2, 4, 24, 2, 2, 2, 6, 8, 6, 12, 24, 2, 2, 2, 2, 2, 12, 4, 6, 8, 2, 2, 8, 8, 2, 4, 2, 24, 2, 2, 6, 4

Offset

1,3

Comments

Frequently equal, but not identical, to A009223 (i.e. GCD of sigma and phi of n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..23374

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Formula

a(n) = gcd(A048250(n), A023900(n)) = gcd(A000203(A007947(n)), A000010(A007947(n))).

a(n) = A322360(n) / A322359(n). - Antti Karttunen, Dec 04 2018

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] g1[x_] := GCD[DivisorSigma[1, x], EulerPhi[x]] g2[x_] := GCD[DivisorSigma[1, cor[x]], EulerPhi[cor[x]]] Table[g2[w], {w, 1, 128}]
a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, GCD[Times@@((#-1)& @@@ f), Times@@((#+1)& @@@ f)]]]; Array[a, 100] (* Amiram Eldar, Dec 05 2018 *)

Prog

(PARI) a(n)=my(f=factor(n)[, 1]); gcd(prod(i=1, #f, f[i]+1), prod(i=1, #f, f[i]-1)) \\ Charles R Greathouse IV, Feb 14 2013

Crossrefs

Cf. A048250, A173557, A023900, A000203, A007947, A000010, A009223, A066087, A322359, A322360, A322362.

Sequence in context: A068068 A193523 A092505 * A323406 A160520 A235708

Adjacent sequences: A066083 A066084 A066085 * A066087 A066088 A066089

Keyword

nonn

Author

Labos Elemer, Dec 04 2001

Extensions

Name edited, part of the old name transferred to the formula section by Antti Karttunen, Dec 04 2018

Status

approved